Explicit expression for modular kernel. The explicit expression for the four-point conformal block was obtained by a tedious work in [1]}, [2]} and has the form
\(K(a,a^{\prime };a_i,b)=4\sinh (2\pi a^{\prime }/b )\sinh (2\pi ba^{\prime } ) {S_b(u_1)S_b(u_2)\over S_b(v_1)S_b(v_2)}\int {\rm d}x \prod _{i=1}^4{S_b(x-\xi _i)\over S_b(x-\zeta _i)},\) 
